Question: The following line passes through point $(4, 8)$ : $y = \dfrac{15}{7} x + b$ What is the value of the $y$ -intercept $b$ ?
Answer: Substituting $(4, 8)$ into the equation gives: $8 = \dfrac{15}{7} \cdot 4 + b$ $8 = \dfrac{60}{7} + b$ $b = 8 - \dfrac{60}{7}$ $b = -\dfrac{4}{7}$ Plugging in $-\dfrac{4}{7}$ for $b$, we get $y = \dfrac{15}{7} x - \dfrac{4}{7}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(4, 8)$